Sensitivity analysis of flexible multibody systems with nonlinear beams

Resumo

Optimization of the dynamics of multibody systems is an active area of research with many important applications in different fields. Among many available optimization techniques, gradient methods are very versatile and popular; and one of its main ingredients is the computation of sensitivities. Sensitivities provides information about how the coordinates of the system change with time when the parameters change. Since multibody systems are typically represented by systems of nonlinear differential equations (or algebraic-differential systems), sensitivities are computed evaluating the corresponding derivatives respect the parameters around the reference movement. These derivatives (sensitivities) depends on time and are the solutions of a system of linear differential
equations (with variable coefficients). Their computation may be performed after the solution for the dynamics, or simultaneously with it. Sensitivity analysis of mechanisms exclusively composed by rigid bodies has been studied in many works of the literature. However, analysis dealing with flexible mechanisms are rarer. In this work we show the results of a sensitivity analysis of special systems, where the flexible parts are slender beams represented by a nonlinear beam model. Their sensitivity contributions are computed analytically improving the efficiency and accuracy of the computations. What is more, a robust and physically intuitive approach based on a finite-difference method is presented for obtaining preliminary sensitivity results, that provide a valuable tool for developing and validate the previously described analytical approach. Some simple numerical examples are presented showing the performance of the proposed approach.